Finite Group Databasebeta

← Group #13150860

Character table — Group #13150860

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222344446666666121212123366666612121212121212123666666666661212121212121212121212122222444444446666666612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11-11-11-1-1-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-11-11-11-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-1-1-11111111-1-1-1-1-1-111-1-111-1-1-1-111
χ61111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-11-11111-1-111-1-1-1-1-1-111-1-11111-1-1
χ71111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ81111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ91111-1-1111-1-11-1-1-1-11111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-11-111-1-11-11-1-1111-1-1111111-1-1-1-1-1-111-1-111-1-1
χ101111-1-1111-1-11-1-1-1-11111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-11-1-1-111-111-11-111-1-1-1-1-1-111-1-11111-1-111-1-111
χ111111-1-1111-1-11-1-1-1-11111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-111-1-1111-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111
χ121111-1-1111-1-11-1-1-1-11111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-11-111-1-1-1-1111-1-111-1-111-1-111111111-1-1-1-1-1-1
χ131111-1-11-1-1111-1-1-1-111-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-111111-11-1-11-1-1-111111-1-111-1-1-1-111-1-1111111-1-1-1-1
χ141111-1-11-1-1111-1-1-1-111-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-111111-1-111-111-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ151111-1-11-1-1111-1-1-1-111-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-11111-1111-1-1-111-11-1-1-111111111-1-1-1-111-1-1-1-1-1-111
χ161111-1-11-1-1111-1-1-1-111-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-11111-11-1-1111-11-1-11-1-111-1-1-1-111-1-111-1-1111111-1-1
χ1722222222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000202020002000000-1-100000000-1-1-1-100-1-1
χ1822222222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000-20-20-2000-2000000110000000011110011
χ192222222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10020202000200000-1-1000000-1-1-1-10000-1-100
χ202222222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100-20-20-2000-20000011000000111100001100
χ212222222-2-2-2-22222222-2-2-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-111-2-2111111110002020-2000-2000000-1-10000000011-1-10011
χ222222222-2-2-2-22222222-2-2-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-111-2-211111111000-20-20200020000001100000000-1-11100-1-1
χ232222222-2-2-2-22222222-2-2-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-21111111111002020-2000-200000-1-1000000-1-11100001100
χ242222222-2-2-2-22222222-2-2-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-2111111111100-20-2020002000001100000011-1-10000-1-100
χ252222-2-2222-2-22-2-2-2-22222-2-22-122-1-12-122221111-1-2-211-1-11111-1-1-1-2-2-1-1-1-1111100020-20-20002000000-1-100000000-1-1110011
χ262222-2-2222-2-22-2-2-2-22222-2-22-122-1-12-122221111-1-2-211-1-11111-1-1-1-2-2-1-1-1-11111000-20202000-2000000110000000011-1-100-1-1
χ272222-2-2222-2-22-2-2-2-22222-2-2-12-1-122-12-1-1-1-1-2-2-2-2-111-2-2-1-11111-12211-1-1-1-111110020-202000-200000-1-100000011110000-1-100
χ282222-2-2222-2-22-2-2-2-22222-2-2-12-1-122-12-1-1-1-1-2-2-2-2-111-2-2-1-11111-12211-1-1-1-1111100-2020-200020000011000000-1-1-1-100001100
χ292222-2-22-2-2222-2-2-2-222-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-1-2-211-1-11111-111221111-1-1-1-100020-202000-2000000-1-100000000111100-1-1
χ302222-2-22-2-2222-2-2-2-222-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-1-2-211-1-11111-111221111-1-1-1-1000-2020-200020000001100000000-1-1-1-10011
χ312222-2-22-2-2222-2-2-2-222-2-222-12-1-122-1211112222-111-2-2-1-11111-1-2-2-1-11111-1-1-1-10020-20-2000200000-1-100000011-1-100001100
χ322222-2-22-2-2222-2-2-2-222-2-222-12-1-122-1211112222-111-2-2-1-11111-1-2-2-1-11111-1-1-1-100-20202000-20000011000000-1-1110000-1-100
χ3322-2-22-222i−2i2i−2i222-2-2-2-22i−2i2i−2i222-22-2-2-22i2i−2i−2i2i2i−2i−2i22-22-22-222-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3422-2-22-222i−2i2i−2i222-2-2-2-22i−2i2i−2i2-12-2-11-212i2i−2i−2i−i−iii-12-2-11-11-1-1111−ii2i−2i−i−iii−i−iii000000000000000000−i3i3000000003−3−i3i3003−3
χ3522-2-22-222i−2i2i−2i222-2-2-2-22i−2i2i−2i2-12-2-11-212i2i−2i−2i−i−iii-12-2-11-11-1-1111−ii2i−2i−i−iii−i−iii000000000000000000i3−i300000000−33i3−i300−33
χ3622-2-22-222i−2i2i−2i222-2-2-2-22i−2i2i−2i-12-112-21-2−i−iii2i2i−2i−2i-1-112-2-11-1-11112i−2i−ii−i−iii−i−iii0000000000000000−i3i3000000−i3i33−300003−300
χ3722-2-22-222i−2i2i−2i222-2-2-2-22i−2i2i−2i-12-112-21-2−i−iii2i2i−2i−2i-1-112-2-11-1-11112i−2i−ii−i−iii−i−iii0000000000000000i3−i3000000i3−i3−330000−3300
χ3822-2-22-22−2i2i−2i2i222-2-2-2-2−2i2i−2i2i222-22-2-2-2−2i−2i2i2i−2i−2i2i2i22-22-22-222-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3922-2-22-22−2i2i−2i2i222-2-2-2-2−2i2i−2i2i2-12-2-11-21−2i−2i2i2iii−i−i-12-2-11-11-1-1111i−i−2i2iii−i−iii−i−i000000000000000000−i3i300000000−33−i3i300−33
χ4022-2-22-22−2i2i−2i2i222-2-2-2-2−2i2i−2i2i2-12-2-11-21−2i−2i2i2iii−i−i-12-2-11-11-1-1111i−i−2i2iii−i−iii−i−i000000000000000000i3−i3000000003−3i3−i3003−3
χ4122-2-22-22−2i2i−2i2i222-2-2-2-2−2i2i−2i2i-12-112-21-2ii−i−i−2i−2i2i2i-1-112-2-11-1-1111−2i2ii−iii−i−iii−i−i0000000000000000−i3i3000000−i3i3−330000−3300
χ4222-2-22-22−2i2i−2i2i222-2-2-2-2−2i2i−2i2i-12-112-21-2ii−i−i−2i−2i2i2i-1-112-2-11-1-1111−2i2ii−iii−i−iii−i−i0000000000000000i3−i3000000i3−i33−300003−300
χ4322-2-2-2222i−2i−2i2i2-2-222-2-22i−2i−2i2i222-22-2-2-22i2i−2i−2i−2i−2i2i2i2-22-222-2-2-222-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4422-2-2-2222i−2i−2i2i2-2-222-2-22i−2i−2i2i2-12-2-11-212i2i−2i−2iii−i−i-1-221-1-1111-1-11−ii−2i2i−i−iiiii−i−i000000000000000000−i3i3000000003−3i3−i300−33
χ4522-2-2-2222i−2i−2i2i2-2-222-2-22i−2i−2i2i2-12-2-11-212i2i−2i−2iii−i−i-1-221-1-1111-1-11−ii−2i2i−i−iiiii−i−i000000000000000000i3−i300000000−33−i3i3003−3
χ4622-2-2-2222i−2i−2i2i2-2-222-2-22i−2i−2i2i-12-112-21-2−i−iii−2i−2i2i2i-11-1-22-1111-1-112i−2ii−i−i−iiiii−i−i0000000000000000−i3i3000000i3−i3−3300003−300
χ4722-2-2-2222i−2i−2i2i2-2-222-2-22i−2i−2i2i-12-112-21-2−i−iii−2i−2i2i2i-11-1-22-1111-1-112i−2ii−i−i−iiiii−i−i0000000000000000i3−i3000000−i3i33−30000−3300
χ4822-2-2-222−2i2i2i−2i2-2-222-2-2−2i2i2i−2i222-22-2-2-2−2i−2i2i2i2i2i−2i−2i2-22-222-2-2-222-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4922-2-2-222−2i2i2i−2i2-2-222-2-2−2i2i2i−2i2-12-2-11-21−2i−2i2i2i−i−iii-1-221-1-1111-1-11i−i2i−2iii−i−i−i−iii000000000000000000−i3i300000000−33i3−i3003−3
χ5022-2-2-222−2i2i2i−2i2-2-222-2-2−2i2i2i−2i2-12-2-11-21−2i−2i2i2i−i−iii-1-221-1-1111-1-11i−i2i−2iii−i−i−i−iii000000000000000000i3−i3000000003−3−i3i300−33
χ5122-2-2-222−2i2i2i−2i2-2-222-2-2−2i2i2i−2i-12-112-21-2ii−i−i2i2i−2i−2i-11-1-22-1111-1-11−2i2i−iiii−i−i−i−iii0000000000000000−i3i3000000i3−i33−30000−3300
χ5222-2-2-222−2i2i2i−2i2-2-222-2-2−2i2i2i−2i-12-112-21-2ii−i−i2i2i−2i−2i-11-1-22-1111-1-11−2i2i−iiii−i−i−i−iii0000000000000000i3−i3000000−i3i3−3300003−300
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ544444444-4-4-4-44444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-4-4444-4-44-4-4-4-44444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000000000
χ564444-4-44-4-4444-4-4-4-444-4-444-2-2-2-2-2-2-2-22222-2-2-2-21222211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000000000
χ5744-4-44-444i−4i4i−4i444-4-4-4-44i−4i4i−4i-2-2-22-2222−2i−2i2i2i−2i−2i2i2i1-22-221-111-1-1-1−2i2i−2i2iii−i−iii−i−i000000000000000000000000000000000000
χ5844-4-44-44−4i4i−4i4i444-4-4-4-4−4i4i−4i4i-2-2-22-22222i2i−2i−2i2i2i−2i−2i1-22-221-111-1-1-12i−2i2i−2i−i−iii−i−iii000000000000000000000000000000000000
χ5944-4-4-4444i−4i−4i4i4-4-444-4-44i−4i−4i4i-2-2-22-2222−2i−2i2i2i2i2i−2i−2i12-22-21-1-1-111-1−2i2i2i−2iii−i−i−i−iii000000000000000000000000000000000000
χ6044-4-4-444−4i4i4i−4i4-4-444-4-4−4i4i4i−4i-2-2-22-22222i2i−2i−2i−2i−2i2i2i12-22-21-1-1-111-12i−2i−2i2i−i−iiiii−i−i000000000000000000000000000000000000
χ614-44-40040000-400004-4000044-4-4-4-4440000000040000-4-400004000000000000000000000000000000000000000000000000
χ624-44-40040000-400004-400004-2-4-4224-20000−2i32i3−2i32i3-20000220000-200000000−2i32i3−2i32i3000000000000000000000000000000000000
χ634-44-40040000-400004-400004-2-4-4224-200002i3−2i32i3−2i3-20000220000-2000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ644-44-40040000-400004-40000-2422-4-4-24−2i32i3−2i32i30000-20000220000-20000−2i32i3−2i32i30000000000000000000000000000000000000000
χ654-44-40040000-400004-40000-2422-4-4-242i3−2i32i3−2i30000-20000220000-200002i3−2i32i3−2i30000000000000000000000000000000000000000
χ664-44-40040000-400004-40000-2-22222-2-2−2i32i3−2i32i3−2i32i3−2i32i310000-1-13-33-310000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ674-44-40040000-400004-40000-2-22222-2-2−2i32i3−2i32i32i3−2i32i3−2i310000-1-1-33-3310000i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000
χ684-44-40040000-400004-40000-2-22222-2-22i3−2i32i3−2i3−2i32i3−2i32i310000-1-1-33-3310000−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000
χ694-44-40040000-400004-40000-2-22222-2-22i3−2i32i3−2i32i3−2i32i3−2i310000-1-13-33-310000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ704-4-440040000-40000-44000044-44-44-4-40000000040000-440000-4000000000000000000000000000000000000000000000000
χ714-4-440040000-40000-4400004-2-442-2-42000023−23−2323-200002-2000020000000023−23−2323000000000000000000000000000000000000
χ724-4-440040000-40000-4400004-2-442-2-420000−232323−23-200002-20000200000000−232323−23000000000000000000000000000000000000
χ734-4-440040000-40000-440000-242-2-442-423−23−23230000-200002-200002000023−23−23230000000000000000000000000000000000000000
χ744-4-440040000-40000-440000-242-2-442-4−232323−230000-200002-2000020000−232323−230000000000000000000000000000000000000000
χ754-4-440040000-40000-440000-2-22-22-22223−23−232323−23−232310000-113-3-33-10000−333−3−333−3000000000000000000000000000000000000
χ764-4-440040000-40000-440000-2-22-22-22223−23−2323−232323−2310000-11-333-3-10000−333−33−3−33000000000000000000000000000000000000
χ774-4-440040000-40000-440000-2-22-22-222−232323−2323−23−232310000-11-333-3-100003−3−33−333−3000000000000000000000000000000000000
χ784-4-440040000-40000-440000-2-22-22-222−232323−23−232323−2310000-113-3-33-100003−3−333−3−33000000000000000000000000000000000000
χ79666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000220000002200-1-1-1-10000-1-1-1-1000000000000
χ80666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000-2-2000000-2-200111100001111000000000000
χ81666666-3-6-6-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000022000000-2-200-1-1-1-100001111000000000000
χ82666666-3-6-6-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000-2-2000000220011110000-1-1-1-1000000000000
χ836666-6-6-366-6-6-33333-3-3-3-33300000000000000000000000000000000000000002-20000002-200-1-1110000-1-111000000000000
χ846666-6-6-366-6-6-33333-3-3-3-3330000000000000000000000000000000000000000-22000000-220011-1-1000011-1-1000000000000
χ856666-6-6-3-6-666-33333-3-333-3-300000000000000000000000000000000000000002-2000000-2200-1-111000011-1-1000000000000
χ866666-6-6-3-6-666-33333-3-333-3-30000000000000000000000000000000000000000-220000002-20011-1-10000-1-111000000000000
χ8766-6-66-6-36i−6i6i−6i-3-3-33333−3i3i−3i3i0000000000000000000000000000000000000000000000000000−i3i3−i3i300003−33−3000000000000
χ8866-6-66-6-36i−6i6i−6i-3-3-33333−3i3i−3i3i0000000000000000000000000000000000000000000000000000i3−i3i3−i30000−33−33000000000000
χ8966-6-66-6-3−6i6i−6i6i-3-3-333333i−3i3i−3i0000000000000000000000000000000000000000000000000000−i3i3−i3i30000−33−33000000000000
χ9066-6-66-6-3−6i6i−6i6i-3-3-333333i−3i3i−3i0000000000000000000000000000000000000000000000000000i3−i3i3−i300003−33−3000000000000
χ9166-6-6-66-36i−6i−6i6i-333-3-333−3i3i3i−3i0000000000000000000000000000000000000000000000000000−i3i3i3−i300003−3−33000000000000
χ9266-6-6-66-36i−6i−6i6i-333-3-333−3i3i3i−3i0000000000000000000000000000000000000000000000000000i3−i3−i3i30000−333−3000000000000
χ9366-6-6-66-3−6i6i6i−6i-333-3-3333i−3i−3i3i0000000000000000000000000000000000000000000000000000−i3i3i3−i30000−333−3000000000000
χ9466-6-6-66-3−6i6i6i−6i-333-3-3333i−3i−3i3i0000000000000000000000000000000000000000000000000000i3−i3−i3i300003−3−33000000000000
χ9512-1212-1200-600006−6i36i3−6i36i3-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-1200-6000066i3−6i36i3−6i3-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-121200-600006−6i36i36i3−6i36-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121200-6000066i3−6i3−6i36i36-600000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).